Time And Work

Work from Days:If A can do a piece of work in n days, then A's 1 day's work =1/n

Days from Work:If A's 1 day's work =1/n ,then A can finish the work in n days

Concept :

Q. If A can do a piece of work in 10 days and B can complete in 15 days in how many days the work will be completed if they work together.

Let the total work be assumed as LCM(10,15)= 30

Now to complete 30 units A takes 10 daysTo complete 30 units B takes 15 days

Units done in 1 day by A = 3Units done in 1 day by B = 2Units done in 1 day by A & B = 5

To complete 30 units they will take 30/5 = 6days

Ratio:

If A is thrice as good a workman as B, then:Ratio of work done by A and B = 3 : 1.Ratio of times taken by A and B to finish a work = 1 : 3.

Examples : (LCM Concepts)Q 1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together, to do the same job?

A. 4 2/9 days

B. 4 4/9 days

C. 4 5/9 days

D. 4 7/9 days

Q2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?

A. 6 days

B. 4 days

C. 8 days

D. 9 days

Q3. A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?A. 27 days B. 24 daysC. 28 daysD. 29 days

Q4. A and B working separately can do a piece of work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days, the work will be completed?A. 10 ¼ days B. 10 ½ daysC. 8 ¼ daysD. 8 ½ days

Man- Days Concept

(N1*D1*H1)/W1 = (N2*D2*H2)/W2

Examples : (Man-Days Concepts)Q5. 7 spiders can make 7 webs in 7 days. 1 spider will make 1 web in how many days?

A. 1 day B. 7 daysC. 14 daysD. 49 days

Q6. 45 men can complete a work in 16 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?A. 6 days B. 4 daysC. 8 daysD. 9 days

Problems

Q7. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

A.14B.15C.16D.17

Q8. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

A.374B.400C.375D.None

Q9. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

A.8 B.12C.16D.None

Q10. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:

A.15B.25C.30D.None

Q11. If A can complete a work in 12 days, B in 15 days and C can do the same work in 20 days.

i) Working simultaneously they will finish the work in how many days.

ii)A started the work and left after 2 day the remaining work by B in how many days?

iii)A started the work and B joins after 3 days the remaining work will be completed in how many days

iv) If A can complete a work in 12 days, B in 15 days and C can do the same work in 20 days.

v)They started the work together & C left after 2 days, the remaining work will be done in how many days.

vi)They started the work together and B left 2 days before the completion of work after how many days B left.

vii) Working alternatively (A, B, C, A, B, C…..) they will finish the work in how many days.

Q12. If 36 Men can do the work in 18 days then the same work will be done by 18 Men in how many days?

A.32B.36C.18D.None

Q13. 10 woman can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 woman and 10 children take to complete the work.

A.14B.7C.21D.None

Q14. 10 woman can complete a work in 7 days, 10 children take 14 days and 10 men take 21 days to complete the work. How many days will 5 woman, 10 children and 15men take to complete the work?

A.6.67B.4.67C.5.67D.None

Q15. A can complete a work in 10 days. B can complete it in 12 days. If they work on alternate days they can complete the work in how many days if-A starts the work

A.12.6B.11.6C.13.6D.None

Division of wages (Concept)

The wages should be divided based on the work efficiency (no of chocolates eaten) and not the no of days

Q16. A can do a piece of work in 30 days and B can do the same work in 50 days. If they both work together to complete the work and get a total of Rs 800. What should be the share of A and B

A.200,600B.300,500C.500,300D.None